Specifically,
our MPE can be expressed as the masking distance \(\mathbf {E}_{dis}\)  and the masking directions \(\mathbf {E}_{dir}\)  as shown in Fig. REF .
Given an inversed 256\(\times \) 256 binary mask, where one indicates unmasked regions and zero indicates masked regions, we use a 3\(\times \) 3 all-one kernel to calculate the masking distance \(\mathbf {D}_{dis}\)  for each position in masked regions as shown in Fig. REF (b). Then, the distance is clipped and mapped by the Sinusoidal Positional Encoding (SPE) [1]} to get \(\mathbf {E}_{dis}\in \mathbb {R}^{256\times 256\times d}\)
\(\begin{split}\mathbf {E}_{dis,2i}&=\mathrm {sin}(\mathrm {clip}(\mathbf {D}_{dis},0,D_{max})/10000^{\frac{i}{d}}),\\\mathbf {E}_{dis,2i+1}&=\mathrm {cos}(\mathrm {clip}(\mathbf {D}_{dis},0,D_{max})/10000^{\frac{i}{d}}),\end{split}\) 
